Innermost stable circular orbits of charged spinning test particles

The effects of a paritcle's spin and electric charge on its angular momentum, energy and radius on the innermost stable circular orbit are investigated based on the particle's equations of motion in a background of the Kerr-Newmann spacetime. It is found that the particle's angular momentum and energy have monotonous relationships with not only its spin but also its charge; it is also discovered that the spinning particle's radius may change non-monotonously with its charge. Hence, our result remarkably indicates that particles owning identical spin but different charge may degenerate into a same last stable circular orbit.Comment: 6 page

Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly

We investigate the phase transitions of black holes with conformal anomaly in canonical ensemble from different perspectives. Some interesting and novel phase transition phenomena have been discovered. Firstly, we discuss the behavior of the specific heat and the inverse of the isothermal compressibility. It is shown that there are striking differences in Hawking temperature and phase structure between black holes with conformal anomaly and those without it. In the case with conformal anomaly, there exists local minimum temperature corresponding to the phase transition point. Phase transitions take place not only from an unstable large black hole to a locally stable medium black hole but also from an unstable medium black hole to a locally stable small black hole. Secondly, we probe in details the dependence of phase transitions on the choice of parameters. The results show that black holes with conformal anomaly have much richer phase structure than those without it. There would be two, only one or no phase transition points depending on the parameters we have chosen. The corresponding parameter region are derived both numerically and graphically. Thirdly, geometrothermodynamics are built up to examine the phase structure we have discovered. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges. Furthermore, critical behaviors are investigated by calculating the relevant critical exponents. It is proved that these critical exponents satisfy the thermodynamic scaling laws, leading to the conclusion that critical exponents and the scaling laws can reserve even when we consider conformal anomaly.Comment: some new references adde

Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble

Recently, extended phase space thermodynamics of Lovelock AdS black holes has been of great interest. To provide insight from a different perspective and gain a unified phase transition picture, non-extended phase space thermodynamics of $(n+1)$-dimensional charged topological Lovelock AdS black holes is investigated detailedly in the grand canonical ensemble. Specifically, the specific heat at constant electric potential is calculated and phase transition in the grand canonical ensemble is discussed. To probe the impact of the various parameters, we utilize the control variate method and solve the phase transition condition equation numerically for the case $k=1,-1$. There are two critical points for the case $n=6,k=1$ while there is only one for other cases. For $k=0$, there exists no phase transition point. To figure out the nature of phase transition in the grand canonical ensemble, we carry out an analytic check of the analog form of Ehrenfest equations proposed by Banerjee et al. It is shown that Lovelock AdS black holes in the grand canonical ensemble undergo a second order phase transition. To examine the phase structure in the grand canonical ensemble, we utilize the thermodynamic geometry method and calculate both the Weinhold metric and Ruppeiner metric. It is shown that for both analytic and graphical results that the divergence structure of the Ruppeiner scalar curvature coincides with that of the specific heat. Our research provides one more example that Ruppeiner metric serves as a wonderful tool to probe the phase structures of black holes

P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity

To understand the effect of third order Lovelock gravity, $P-V$ criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and details than the former literature. A detailed analysis of the limit case $\beta\rightarrow\infty$ is performed for the seven-dimensional black holes. It is shown that for the spherical topology, $P-V$ criticality exists for both the uncharged and charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P-V$ criticality. It may be attributed to the effect of higher derivative terms of curvature because similar phenomenon was also found for Gauss-Bonnet black holes. For $k=0$, there would be no $P-V$ criticality. Interesting findings occur in the case $k=-1$, in which positive solutions of critical points are found for both the uncharged and charged cases. However, the $P-v$ diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of entropy. It is shown that for any nontrivial value of $\alpha$, the entropy is always positive for any specific volume $v$. Since no $P-V$ criticality exists for $k=-1$ in Einstein gravity and Gauss-Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which is absent in the Gauss-Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of entropy. We also check the Gibbs free energy graph and the "swallow tail" behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.Comment: 13 pages, 7 figure

P-V criticality of conformal anomaly corrected AdS black holes

The effects of conformal anomaly on the thermodynamics of black holes are investigated in this Letter from the perspective of $P-V$ criticality of AdS black holes. Treating the cosmological constant as thermodynamic pressure, we extend the recent research to the extended phase space. Firstly, we study the $P$-$V$ criticality of the uncharged AdS black holes with conformal anomaly and find that conformal anomaly does not influence whether there exists Van der Waals like critical behavior. Secondly, we investigate the $P$-$V$ criticality of the charged cases and find that conformal anomaly influences not only the critical physical quantities but also the ratio $\frac{P_cr_c}{T_c}$. The ratio is no longer a constant as before but a function of conformal anomaly parameter $\tilde{\alpha}$. We also show that the conformal parameter should satisfy a certain range to guarantee the existence of critical point that has physical meaning. Our results show the effects of conformal anomaly

Observational constraint on the interacting dark energy models including the Sandage-Loeb test

Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We find that the inclusion of SL test can obviously provide more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term including the SL test is estimated at $\delta=-0.01 \pm 0.01 (1\sigma) \pm 0.02 (2\sigma)$, which has been improved to be only a half of original scale on corresponding errors. Comparing with the combination of SNIa and OHD, we find that the inclusion of SL test directly reduces the best-fit of interaction from 0.39 to 0.10, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of interaction. For the varying coupling model, we reconstruct the interaction $\delta (z)$, and find that the interaction is also negative similar as the constant coupling model. However, for high redshift, the interaction generally vanishes at infinity. The constraint result also shows that the $\Lambda$CDM model still behaves a good fit to the observational data, and the coincidence problem is still quite severe. However, the phantom-like dark energy with $w_X<-1$ is slightly favored over the $\Lambda$CDM model.Comment: 10 pages, 7 figure

Holographic thermalization with a chemical potential in Gauss-Bonnet gravity

Holographic thermalization is studied in the framework of Einstein-Maxwell-Gauss-Bonnet gravity. We use the two-point correlation function and expectation value of Wilson loop, which are dual to the renormalized geodesic length and minimal area surface in the bulk, to probe the thermalization. The numeric result shows that larger the Gauss-Bonnet coefficient is, shorter the thermalization time is, and larger the charge is, longer the thermalization time is, which implies that the Gauss-Bonnet coefficient can accelerate the thermalization while the charge has an opposite effect. In addition, we obtain the functions with respect to the thermalization time for both the thermalization probes at a fixed charge and Gauss-Bonnet coefficient, and on the basis of these functions, we obtain the thermalization velocity, which shows that the thermalization process is non-monotonic. At the middle and later periods of the thermalization process, we find that there is a phase transition point, which divides the thermalization into an acceleration phase and a deceleration phase. We also study the effect of the charge and Gauss-Bonnet coefficient on the phase transition point.Comment: 23 pages, many figures,footnote 4 is modified. arXiv admin note: substantial text overlap with arXiv:1305.484

Holographic thermalization in noncommutative geometry

Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.Comment: some materials have been delete